I wasn't doing anything as intense as p90x when I went low carb clean paleo for the first time (I vary between paleo/primal, lower/higher carbs depending on how I feel). Basically I was just doing normal heavy and quite dense/intense weightlifting. First 4-5 weeks were horrible - I had to reduce the weights, reps and was feeling totally demotivated. Afterwards, however, my strength/energy came back and it's been constantly quite good since - whether I eat low/higher carb or paleo/primal.
Hope time will help you too. And may be a higher amount of "good carbs", if you can/want to include them.